1. Field of the Invention
The present invention relates to a piezoelectric resonator, a method of manufacturing such a piezoelectric resonator, and a filter, a duplexer, and a communication device using such a piezoelectric resonator. More specifically, the present invention relates to a piezoelectric resonator improved so as to be able to remove spurious components, a method of manufacturing such a piezoelectric resonator, and a filter, a duplexer, and a communication device using such a piezoelectric resonator.
2. Description of the Background Art
Components incorporated in electronic devices such as cellular phones are required to be small in size and weight. For example, a filter for use in a cellular phone is required to be small in size and be precisely adjusted in frequency characteristic.
One of known filters satisfying such requirements is a filter using a piezoelectric resonator (for example, refer to Japanese Patent Laid-Open Publication No. 60-68711, pp. 2-4, FIGS. 3 and 4).
FIG. 14A is a section view of a basic structure of a conventional piezoelectric resonator. In FIG. 14A, a piezoelectric resonator 710 is provided on a substrate 705. On the substrate 705, a cavity 704 is formed by partially etching from the underside of the substrate 705 through a fine processing scheme. The piezoeletric resonator 710 includes a piezoeletric body 701, which is a main component of the resonator, and an upper electrode 702 and a lower electrode 703 that are provided above and below, respectively, the piezoelectric body 701.
The hollow cavity 704 is provided in the substrate 705 in order to ensure vibrations of the piezoeletric resonator 710.
The piezoeletric resonator 710 is applied with an electric field in a thickness direction via the upper electrode 702 and the lower electrode 703 that are provided above and below, respectively, the piezoelectric body 701. With this, the piezoeletric resonator 710 vibrates in the thickness direction.
The operation of the piezoeletric resonator 710 is described below by using vertical vibrations in the thickness direction on an infinite plane. FIG. 14B is a schematic perspective view for describing the operation of the piezoeletric resonator 710. As shown in FIG. 14B, when an electric field is applied to the upper electrode 702 and the lower electrode 703, electric energy is transformed to mechanical energy at the piezoeletric body 701. The excited mechanical vibrations are vibrations expanding in the thickness direction, and therefore the piezoeletric body 701 expands in a direction of the electric field.
When the thickness of the piezoeletric resonator 710 is t, the piezoeletric resonator 710 uses resonant vibrations in the thickness of the piezoeletric body 701 to produce resonance at a resonant frequency of fr1 (=v/λ) corresponding to a wavelength λ satisfying t=λ/2. Here, v is an average of ultrasonic velocity in the material forming the piezoeletric resonator 710.
In the structure of the piezoeletric resonator 710 shown in FIG. 14, with the cavity 704 being formed, vertical vibrations in the thickness direction of the piezoeletric body 701 are ensured.
FIG. 14C is a diagram of an equivalent circuit of the piezoeletric resonator 710. As shown in FIG. 14C, the equivalent circuit of the piezoeletric resonator 710 includes a serial resonant circuit and a parallel resonant circuit. That is, the equivalent circuit includes a serial resonant circuit formed of a capacitor (C1), an inductor (L1), and a resistor (R1), and a parallel resonant circuit formed of a capacitor (C0) connected in parallel to the serial resonant circuit. Therefore, the piezoeletric resonator 710 has a resonant frequency and an anti-resonant frequency. FIG. 14D is a graph showing a frequency characteristic of admittance in the equivalent circuit shown in FIG. 14C. As shown in FIG. 14D, admittance is maximum at a resonant frequency of fr1 and minimum at an anti-resonant frequency of fa1. Here, fr1 and fa1 have the following relation.
            fr      ⁢                          ⁢      1        =          1              2        ⁢                                  ⁢        π        ⁢                              L            ⁢                                                  ⁢                          1              ·              C                        ⁢                                                  ⁢            1                                          f      ⁢                          ⁢      a      ⁢                          ⁢      1        =          fr      ⁢                        1          +                                    C              ⁢                                                          ⁢              1                                      C              ⁢                                                          ⁢              0                                          
When the piezoelectric resonator 710 is applied to a filter by using the frequency characteristic of the admittance, a small-sized filter with low loss using resonant vibration of the piezoelectric body can be achieved.
In practice, since the piezoelectric resonator is partially fixed to the substrate, the entire piezoelectric resonator does not make free vertical vibrations. The vibrating portion is divided, as shown in FIG. 14A, into a vibrating region fixed to a peripheral portion of the cavity 704 and a vibrating region with its both ends vibrating as free ends, such as an upper portion of the cavity.
In the vibrating portion, vibration defined by the thickness of the vibrating portion is exited as main resonant vibration. The vibrating portion is fixed to the periphery of the cavity, and the fixed portion is actually not completely fixed as fixed end. Therefore, the main resonant vibration having a frequency of f1 is propagated to the substrate via the fixed portion. As a result, depending on how the vibrating portion is supported and fixed, in addition of desired vertical vibration in the thickness direction in a fundamental mode (hereinafter referred to as a ½ wavelength mode with its frequency of f1), spurious vibration having a frequency near the frequency f1 of the main resonant frequency occurs.
The reason for occurrence of such spurious vibration is that spurious vibration is excited by a leak of vibration of the fixed portion to the substrate. Here, it is assumed that a resonant frequency of the spurious vibration is near the main resonant frequency of the main resonant vibration. With the main resonant vibration leaked to the substrate, spurious vibration occurs. Since it is assumed that the resonant frequency of the spurious vibration is near the main resonant frequency, the spurious vibration causes a spurious resonant frequency to occur near the main resonant frequency. FIG. 15A is a graph showing a frequency characteristic of admittance when spurious vibration is present. As shown in FIG. 15A, spurious vibration, that is, a spurious resonant frequency 713, is present between the resonant frequency fr1 and the anti-resonant frequency fa1.
FIG. 15B is a circuit diagram showing the structure of a filter using a piezoelectric resonator. FIG. 15C is a diagram showing a frequency passing characteristic when the piezoelectric resonator with the spurious resonant frequency 713 is used for the filter as shown in FIG. 15B.
As shown in FIG. 15B, when piezoelectric resonators having the spurious resonant frequency 713 are connected to each other in parallel and to another resonator in series to form a filter, a frequency passing characteristic (skirt characteristic) having two abrupt attenuation poles can be achieved. However, due to the spurious resonant frequency 713, unevenness 714 occurs in a pass-band. If such a filter having the unevenness 714 is used, a signal passing the evenness 714 becomes at a signal larger or smaller than a designed level. As a result, quality degradation in communications occurs.
In general, what is important for the filter is that no spurious resonant frequency is present in a desired band. Therefore, it is required for the serial resonator and the parallel resonator forming a filter not to generate a spurious resonant frequency in the desired band.